# ScoreStop: Gradient-based early stopping using functional score tests

arXiv: https://arxiv.org/abs/2606.02740 · HTML: https://mlsanity.com/paper/2606.02740/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Early Stopping without a Validation Set](https://mlsanity.com/paper/1703.09580/) (2017)
- [Early stopping for kernel boosting algorithms: A general analysis with localized complexities](https://mlsanity.com/paper/1707.01543/) (2017)
- [Inference on function-valued parameters using a restricted score test](https://mlsanity.com/paper/2105.06646/) (2021)
- [Stopping Rules for Stochastic Gradient Descent via Anytime-Valid Confidence Sequences](https://mlsanity.com/paper/2512.13123/) (2025)
- [A Researcher's Guide to Empirical Risk Minimization](https://mlsanity.com/paper/2602.21501/) (2026)
- [Towards E-Value Based Stopping Rules for Bayesian Deep Ensembles](https://mlsanity.com/paper/2604.18089/) (2026)

## Abstract (arXiv)

Gradient boosted decision trees require a stopping rule to avoid overfitting. The standard rule monitors a validation loss and stops if the loss fails to improve for a fixed patience period. However, the patience parameter has no interpretable scale and validation losses can be noisy or implicitly defined by a user-specified gradient. We propose ScoreStop, a gradient-based early-stopping rule that casts the stopping decision at each iteration as a test of the null hypothesis that the current predictor is the population risk minimizer. We use a functional score test, computed on validation data, with a statistic that is scale-invariant in the update direction, with a known asymptotic distribution under the null. Because our test uses gradients rather than loss values, the same construction applies to implicit losses such as LambdaRank, and data-dependent losses such as Cox regression via influence functions. In synthetic experiments and real-data benchmarks, we show that ScoreStop is competitive with loss-based methods.